Jet coronation: Coexistence of compressible and incompressible dynamics

This paper, recognized with a 2025 APS DFD Gallery of Fluid Motion Award, investigates the coexistence of compressible and incompressible dynamics in jet coronation.

The Gist

Imagine you have a glass test tube partially filled with oil, and you drop it onto a hard floor. You might expect it to just splash a little or make a mess. But according to this study, when that tube hits the ground, the liquid inside doesn't just splash; it performs a complex, high-speed dance that involves two very different types of physics happening at the same time: the "sloshing" of a normal liquid and the "squeezing" of a compressible fluid.

Here is a breakdown of what the researchers found, using everyday analogies:

The Setup: A Sudden Stop

Think of the liquid inside the tube like a crowd of people running down a hallway. When the tube hits the floor, the bottom of the tube stops instantly, but the liquid keeps moving forward due to momentum. It's like a sudden traffic jam where everyone rushes toward the front. This creates a massive, invisible pressure wave that shoots up through the liquid.

The Main Act: The "Jet" and the "Crown"

When this pressure wave hits the surface of the liquid, it doesn't just ripple; it launches a dramatic display:

1. The Central Jet (The Spear): In the very center, the liquid is forced upward into a thin, super-fast spear. This is the "focused jet." It's smooth and straight, like a high-pressure water hose nozzle.
2. The Crown (The Umbrella): Surrounding that central spear, a ring of liquid shoots out and up, forming a shape that looks like a crown or an upside-down umbrella. This is the "annular sheet."

The Twist: The "Fluid Fishbones"

Here is where it gets weird. As that "crown" ring expands upward, its edge (the rim) doesn't stay smooth. It starts to wiggle and ripple, forming little bumps and waves that look like the bones of a fish or the spine of a skeleton.

The researchers call this a "fluid-chain" mechanism. Imagine a rubber band that you stretch; if you wiggle it just right, it forms little loops. In this experiment, as the liquid ring slows down and tries to pull back, the liquid redistributes itself, causing those wiggly "fishbone" patterns to grow. It's a battle between the liquid's inertia (wanting to keep moving) and surface tension (trying to hold the shape together).

The Hidden Player: The "Ghost Bubbles"

While the jet and crown are doing their dance, something invisible is happening deep inside the liquid. The intense pressure changes cause tiny pockets of vapor (bubbles) to appear and disappear rapidly beneath the surface.

Think of these like "ghost bubbles." They pop into existence when the pressure drops and vanish when the pressure spikes. The paper suggests that the violent popping and collapsing of these bubbles might be shaking the liquid enough to help create or distort the "crown" and its wiggly edges. It's as if the liquid is breathing in and out violently, and that breathing is affecting the shape of the splash.

The Big Picture: Two Worlds Colliding

The most important takeaway from this paper is that this single event is a mix of two different worlds of physics:

• The Incompressible World: This is the "sloshing" part where the liquid acts like a solid block of water, forming the smooth jet and the expanding crown.
• The Compressible World: This is the "squeezing" part where the liquid acts like a gas, creating those vapor bubbles and pressure waves.

Usually, scientists study these separately. This paper shows that in a high-speed impact, they happen simultaneously and influence each other. The "squeezing" (bubbles) and the "sloshing" (jet/crown) are locked in a complex, nonlinear relationship.

What They Did

The researchers filmed this event using super-fast cameras (taking 30,000 pictures per second) to catch these split-second moments. They dropped glass tubes filled with silicone oil onto a steel plate and watched how the liquid reacted. They didn't just look at the splash; they tracked the height of the jet, the size of the crown, and the volume of the invisible bubbles to see how they moved together over time.

In short: When you drop a liquid-filled tube, you get a high-speed spear of liquid surrounded by a wiggly, fishbone-edged crown, all while invisible bubbles pop and collapse underneath, proving that liquids can be both "solid-like" and "gas-like" at the exact same time.

Technical Summary

Technical Summary: Jet Coronation: Coexistence of Compressible and Incompressible Dynamics

Problem Statement
The impact of a liquid-filled container on a rigid substrate generates a complex spectrum of transient hydrodynamic phenomena, including jet focusing, crown formation, interfacial instabilities, and cavitation. While previous research has established the existence of these regimes—ranging from smooth, axisymmetric jets to complex atomization and vapor cavity formation—the specific interplay between inertial focusing (often treated as incompressible) and local compressible effects (such as acoustic waves and cavitation) remains a subject of investigation. Specifically, the mechanisms governing the coexistence of a focused central jet, an expanding annular liquid sheet (crown), and cavitation bubbles within the same flow field require further elucidation.

Methodology
The study employs high-speed visualization to investigate the "crown-jet" regime, where a focused jet, an annular sheet, and cavitation coexist. The experimental setup involves a cylindrical glass test tube (inner diameter $D = 14.2$ mm) partially filled with silicone oil (kinematic viscosity $\nu = 10$ mm$^2$/s, surface tension $\gamma \approx 20\text{--}21$ mN/m). The tube is dropped from a height of $H = 135$ mm onto a rigid steel substrate, achieving a nominal impact velocity of $U_0 \approx 1.63$ m/s.

To capture the rapid dynamics, two synchronized high-speed cameras (Photron FASTCAM SA-X) were utilized:

1. One camera focused on the air–liquid interface and jet tip at 30,000 fps with a spatial resolution of 0.037 mm/pixel.
2. A second camera monitored the bulk liquid column and cavitation bubbles at 20,000 fps with a resolution of 0.321 mm/pixel.

This dual-configuration approach allowed for the simultaneous observation of fine interfacial structures and large-scale bulk dynamics, including the evolution of vapor cavities.

Key Results
The experiments reveal a distinct regime characterized by the simultaneous occurrence of three phenomena:

1. Focused Jet Formation: Immediately upon impact ($t=0$), a slender, highly focused liquid jet emerges from the concave air–liquid interface, driven by inertial focusing of the surrounding liquid toward the central axis.
2. Annular Sheet and Crown Dynamics: Approximately 2.3 ms post-impact, a thin annular liquid sheet develops around the primary jet, expanding upward to form a crown. Unlike regimes where the sheet remains smooth (as seen in weaker impacts), the rim of this crown exhibits significant circumferential perturbations. These azimuthal modulations amplify progressively, resembling a "fluid-chain" mechanism where rim retraction and local mass conservation drive the development of corrugations.
3. Cavitation Coupling: The formation of the crown and the growth of rim instabilities occur simultaneously with the quasi-periodic disappearance and reappearance of a vapor cavity beneath the interface. The total cavitation volume exhibits significant temporal fluctuations.

The study observes a strong coupling between the pressure waves generated by the collapse of cavitation bubbles and the formation of the crown from the base of the air–liquid interface. The high positive pressure associated with bubble collapse appears to influence the dynamics of the liquid sheet.

Key Contributions

• Visualization of Coexistence: The paper provides high-resolution visualization of a regime where compressible dynamics (cavitation and pressure waves) and incompressible dynamics (inertial focusing and free-surface motion) coexist within the same system.
• Rim Instability Characterization: It details the development of azimuthal instabilities on the crown rim, linking them to a fluid-chain-like mechanism driven by rim retraction, distinct from the smoother dynamics observed in purely radial expansion regimes.
• Coupling Mechanism: The work highlights the temporal correlation between cavitation volume fluctuations and crown development, suggesting a feedback loop between bubble collapse pressure waves and interfacial sheet formation.

Significance and Claims
The authors assert that this study visualizes and highlights the diverse mechanisms arising during container impact, specifically focusing on the complex interplay between incompressible interfacial dynamics and locally compressible effects. The observed coupling underscores the highly nonlinear nature of the flow.

The paper maintains a modest stance regarding the causal mechanisms. While it suggests a possible relationship between the crown structures and the growth/collapse of cavitation bubbles, the authors explicitly state that the detailed mechanism remains unclear. They identify the clarification of this coupling as an important direction for future work requiring more comprehensive investigation, rather than claiming to have fully resolved the physics of the interaction.